9 1 Angle Relationships Warm Up Problem of

9 -1 Angle Relationships Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

9 -1 Angle Relationships Warm Up Solve. 1. x + 30 = 90 x = 60 2. 103 + x = 180 x = 77 3. 32 + x = 180 x = 148 4. 90 = 61 + x x = 29 5. x + 20 = 90 x = 70

9 -1 Angle Relationships Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, 1 of the class wants sausage on the 3 pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza? 1 6

9 -1 Angle Relationships Sunshine State Standards MA. 8. G. 2. 2 Classify and determine the measure of angles, …

9 -1 Angle Relationships angle Vocabulary adjacent angles right angle supplementary angles acute angle complementary angles obtuse angle straight angle vertical angles congruent angles

9 -1 Angle Relationships An angle ( ) is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.

9 -1 Angle Relationships

9 -1 Angle Relationships Additional Example 1: Classifying Angles Use the diagram to name each figure. A. two acute angles TQP, RQS m TQP = 43°; m RQS = 47° B. two obtuse angles SQP, RQT m SQP= 133°; m RQT = 137°

9 -1 Angle Relationships Additional Example 1: Classifying Angles Use the diagram to name each figure. C. a pair of complementary angles TQP, RQS m TQP + m RQS = 43° + 47° = 90 B. two pairs of supplementary angles TQP, TQR m TQP + m TQR = 43° + 137° = 180 SQP, SQR m SQP + m SQR = 133° + 47° = 180

9 -1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. A. two acute angles AEB measures 58° and DEC measures 58° B. two obtuse angles AEC measures 148° and DEB measures 122°

9 -1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. C. a pair of complementary angles AEB measures 58° and DEC measures 32°. 58 + 32 = 90° D. a pair of supplementary angles AEC measures 148° and DEC measures 32°. 148 + 32 = 180°; AEB measures 58° and DEB measures 122°, 58 + 122 = 180°

9 -1 Angle Relationships Additional Example 2 A: Finding Angle Measures Use the diagram to find each angle measure. If m 1 = 37°, find m 2. m 1 + m 2 = 180° 1 and 2 are supplementary. 37° + m 2= 180° Substitute 37 for m 1. Subtract 37 from both sides. – 37° m 2 = 143°

9 -1 Angle Relationships Additional Example 2 B: Finding Angle Measures Use the diagram to find each angle measure. Find m 3 = 37°. m 2 + m 3 = 180° 2 and 3 are supplementary. 143° + m 3 = 180° Substitute 143 for m 2. Subtract 143 from both sides. – 143° m 3 = 37°

9 -1 Angle Relationships Check It Out: Example 2 A Use the diagram to find each angle measure. If m 3 = 142°, find m 4. m 3 + m 4 = 180° 142° + m 4= 180° – 142° m 4 = 38°

9 -1 Angle Relationships Check It Out: Example 2 B Use the diagram to find each angle measure. Find m 1 + m 4 = 180° m 1 + 38° = 180° – 38° m 1 – 38° = 142°

9 -1 Angle Relationships Adjacent angles have a common vertex and a common side, but no common interior points. Angles 1 and 2 in the diagram are adjacent angles. Congruent angles have the same measure. Vertical angles are the nonadjacent angles formed by two intersecting lines. Angles 2 and 4 are vertical angles. Vertical angles are congruent.

9 -1 Angle Relationships Additional Example 3: Application A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 1: Find m CBD. ABF CBD m ABF = m CBD = 26 Vertical angles are congruent. Congruent angles have the same measure. Substitute 26 for m CBD.

9 -1 Angle Relationships Additional Example 3 Continued A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 2: Find m DBE. m CBD + m DEB = 90° The angles are complementary. 26 + m DEB = 90° Substitute 26 for m CBD. – 26° Subtract 26 from both sides. m DEB = 64°

9 -1 Angle Relationships Check It Out: Example 3 Based on the map, what is the measure of BGC? AGB is congruent to EGF. m AGB = 42° m BGC + m AGB = 90° m BGC + 42° = 90° m BGC = 48°

9 -1 Angle Relationships Lesson Quizzes Standard Lesson Quiz for Student Response Systems

9 -1 Angle Relationships Lesson Quiz Use the diagram to name each figure or find each angle measure. 1. a right angle Possible answer: CGD 2. two acute angles Possible answer: 1, 2 3. pair of complementary angles Possible answer: 3, 4 4. If m 1 = 47°, then find m 3. 47° 5. Find m 4. 43°

9 -1 Angle Relationships Lesson Quiz for Student Response Systems 1. If m 1 = 42°, then find m 3. A. 3° B. 42° C. 48° D. 90°

9 -1 Angle Relationships Lesson Quiz for Student Response Systems 2. Name a pair of complementary angles. A. CGD B. AGF C. AGB, BGC D. CGD, DGF

9 -1 Angle Relationships Lesson Quiz for Student Response Systems 3. Find m CGD. A. 3° B. 42° C. 90° D. 180°